Two cars adjacent to each other on a highway. The first car accelerates uniformly at 3m/s2 the moment the light turns green. The second car is moving at 18m/s and is beside the first car at the instant the light changes and continues driving with a constant velocity. When are the cars side by side again?

Write equations for position from the light (X) vs time (t) and set them equal to each other.
Solve for t.

X1 = (a/2) t^2 = 1.5 t^2
X2 = 18 t

18t = 1.5 t^2

1.5 t (t - 12) = 0

One answer is t=0. What is the other?

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